基于物理信息逆建模框架的密歇根州罗亚尔岛国家公园驼鹿-狼动力学研究：有限且含噪数据下的应用
A physics-informed inverse modeling framework for Moose-Wolf dynamics from limited and noisy data in Isle Royale National Park
- School of Mathematical & Statistical Sciences, IIT Mandi（印度技术学院曼迪分校数学与统计科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出一种基于物理信息的逆建模框架，结合自适应bc-PINN与迁移学习，从罗亚尔岛国家公园1959-2019年驼鹿-狼种群数据中估计非自治捕食者-猎物系统参数，并成功预测2020年驼鹿种群骤降。
AI中文摘要：
驼鹿（Alces alces）与狼（Canis lupus）种群在诸如罗亚尔岛国家公园等生态系统中的相互作用，是捕食者-猎物动力学生态建模的经典基准。数学建模是模拟这些相互作用的有效工具。该领域的核心挑战在于逆问题，即从观测数据中恢复控制系统的参数。尽管经典参数估计方法已取得显著进展，但它们大多依赖数据而非物理，因此在捕捉由环境波动、季节强迫和栖息地变化驱动的生态相互作用的时间变化特性方面存在明显不足。本研究通过求解一个非自治捕食者-猎物系统的逆问题来填补这一空白，该系统包含具有随时间变化的内在增长率和自然死亡率的theta-logistic猎物增长，以及Holling II型和比例依赖的功能响应。采用深度学习框架（具有迁移学习的自适应bc-PINN）直接从种群时间序列数据（1959-2019年）中估计时间依赖和恒定参数。在估计参数之前，我们进行了结构可辨识性分析，以确保模型参数是可辨识的。该框架在两种功能响应下均展示了良好的重建和预测结果。比例依赖模型在训练数据之外展现了更好的预测趋势。我们的框架成功预测了2020年驼鹿种群的突然下降。
英文摘要：
The interaction of moose (Alces alces) and wolf (Canis lupus) populations in ecosystems such as Isle Royale National Park is a canonical benchmark for ecological modeling of prey-predator dynamics. Mathematical modeling is a useful tool for modeling these interactions. A central challenge in this domain is the inverse problem, recovering governing system parameters from observational data. Although classical parameter estimation methods have seen considerable progress, they mostly rely on data rather than physics and therefore largely fall short in capturing the time-varying nature of ecological interactions driven by environmental fluctuations, seasonal forcing, and habitat change. This study addresses that gap by solving the inverse problem for a non-autonomous prey-predator system that incorporates theta-logistic prey growth with temporally varying intrinsic growth and natural death rates, as well as Holling type-II and ratio-dependent functional responses. A deep learning framework (self-adaptive bc-PINN with transfer learning) is employed to estimate time-dependent and constant parameters directly from population time series data (1959-2019). Before estimating the parameters, we performed a structural identifiability analysis to ensure that the model parameters are identifiable. The framework demonstrates good reconstruction and prediction results across both functional responses. The ratio-dependent model has shown the better prediction trend beyond the training data. Our framework successfully predicts the sudden decline in the moose population in 2020.
